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In observational studies, it is typically unrealistic to assume thattreatments are randomly assigned, even conditional on adjusting for allobserved covariates. Therefore, a sensitivity analysis is often needed toexamine how hidden biases due to unobserved covariates would affect inferenceson treatment effects. In matched observational studies where each treated unitis matched to one or multiple untreated controls for observed covariates, theRosenbaum bounds sensitivity analysis is one of the most popular sensitivityanalysis models. In this paper, we show that in the presence of interactionsbetween observed and unobserved covariates, directly applying the Rosenbaumbounds will almost inevitably exaggerate the report of sensitivity of causalconclusions to hidden bias. We give sharper odds ratio bounds to fix thisdeficiency. We illustrate our new method through studying the effect ofanger/hostility tendency on the risk of having heart problems.

Sharpening the Rosenbaum Sensitivity Bounds to Address Concerns About Interactions Between Observed and Unobserved Covariates